The news coverage says he was brought in by request of the mexican government. Note that the request to get Luster back would have been made by the American government -- that's how treaties of extradition work.
Catch my other post where I note that the Mexican government DID sent Luster back -- Dog did not bring him back, because Dog got arrested in Mexico during the abduction.
So in fact there is no evidence that Dog needed to capture him, no evidence of Mexico "refusing" to send Luster back, and every evidence that Mexico would have happily sent Luster back if Dog had simply found him, and told the mexican authorities that he was a wanted man.
But Dog was trying to get $350,000 in bounty for his capture, and was filming for his show.